Answer:
48
Explanation:
You want to know the number of cans 4 inches tall with a volume of 50.24 in³ that will fit on a shelf with a height and depth of 10 inches and a length of 50 inches.
Diameter
The diameter of the can will be found from the volume formula:
V = (π/4)d²h
d = √(4V/(πh)) = √(4·50.24/(4·3.14)) = √16 = 4 . . . inches
The cans are 4 inches in diameter.
Number
The number of cans that will fit in each dimension will be the integer part of the dimension divided by the size of the can in that dimension.
Height: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans high
Depth: (10 in)/(4 in/can) = 2.5 cans . . . . cans will fit 2 cans deep
Length: (50 in/4 in/can) = 12.5 cans . . . . cans will fit 12 cans long
A total of 2 × 2 × 12 = 48 cans will fit on the shelf.
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Additional comment
There will be 2 inches of empty space in each direction.
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